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11-XX Number theory
11Rxx Algebraic number theory: global fields
11R16 Cubic and quartic extensions

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Displaying 1 – 6 of 6

Periodic expansions and units in quadratic and cubic number fields.

Charlotte Goryn Denenberg (1975)

Journal für die reine und angewandte Mathematik

Pólya fields and Pólya numbers

Amandine Leriche (2010)

Actes des rencontres du CIRM

A number field $K$ , with ring of integers $𝒪_{K}$ , is said to be a Pólya field if the $𝒪_{K}$ -algebra formed by the integer-valued polynomials on $𝒪_{K}$ admits a regular basis. In a first part, we focus on fields with degree less than six which are Pólya fields. It is known that a field $K$ is a Pólya field if certain characteristic ideals are principal. Analogously to the classical embedding problem, we consider the embedding of $K$ in a Pólya field. We give a positive answer to this embedding problem by showing that...

Positive inverse Einheiten in komplexen kubischen Zahlkörpern

Reiner Güting (1977)

Acta Arithmetica

Power integral bases in the family of simplest quartic fields.

Olajos, Péter (2005)

Experimental Mathematics

Principalization algorithm via class group structure

Daniel C. Mayer (2014)

Journal de Théorie des Nombres de Bordeaux

For an algebraic number field $K$ with $3$ -class group ${Cl}_{3} (K)$ of type $(3, 3)$ , the structure of the $3$ -class groups ${Cl}_{3} (N_{i})$ of the four unramified cyclic cubic extension fields $N_{i}$ , $1 \leq i \leq 4$ , of $K$ is calculated with the aid of presentations for the metabelian Galois group $G_{3}^{2} (K) = Gal (F_{3}^{2} (K) | K)$ of the second Hilbert $3$ -class field $F_{3}^{2} (K)$ of $K$ . In the case of a quadratic base field $K = ℚ (\sqrt{D})$ it is shown that the structure of the $3$ -class groups of the four $S_{3}$ -fields $N_{1}, ..., N_{4}$ frequently determines the type of principalization of the $3$ -class group of $K$ in $N_{1}, ..., N_{4}$ . This provides...

Purely cubic complex function fields with small units

R. Scheidler (2000)

Acta Arithmetica

Currently displaying 1 – 6 of 6

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